Weighted bounds for multilinear operators with non-smooth kernels

Let $T$ be a multilinear {integral} operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual H\"older continuity of those in the class of multilinear Calder\'on-Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain the bound for the weighted norm of multilinear operators $T$ in terms of $\vec{w}$. As applications, we exploit this result to obtain the weighted bounds {for} certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schr\"odinger operators on $\mathbb{R}^n$ and these results are new in the literature

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BibTeX @unpublished{Bui2015,author={Bui, Anh and Conde-Alonso, Jose and Duong, Xuan Thinh and Hormozi, Mahdi},title={Weighted bounds for multilinear operators with non-smooth kernels},abstract={Let $T$ be a multilinear {integral} operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual H\"older continuity of those in the class of multilinear Calder\'on-Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain the bound for the weighted norm of multilinear operators $T$ in terms of $\vec{w}$. As applications, we exploit this result to obtain the weighted bounds {for} certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schr\"odinger operators on $\mathbb{R}^n$ and these results are new in the literature},year={2015},keywords={Multilinear singular integrals, weighted norm inequaliti es, Lerner’s formual, multilinear Fourier multipliers},note={21},}

RefWorks RT Unpublished MaterialSR ElectronicID 224678A1 Bui, AnhA1 Conde-Alonso, JoseA1 Duong, Xuan ThinhA1 Hormozi, MahdiT1 Weighted bounds for multilinear operators with non-smooth kernelsYR 2015AB Let $T$ be a multilinear {integral} operator which is bounded on certain products of Lebesgue spaces on $\mathbb R^n$. We assume that its associated kernel satisfies some mild regularity condition which is weaker than the usual H\"older continuity of those in the class of multilinear Calder\'on-Zygmund singular integral operators. In this paper, given a suitable multiple weight $\vec{w}$, we obtain the bound for the weighted norm of multilinear operators $T$ in terms of $\vec{w}$. As applications, we exploit this result to obtain the weighted bounds {for} certain singular integral operators such as linear and multilinear Fourier multipliers and the Riesz transforms associated to Schr\"odinger operators on $\mathbb{R}^n$ and these results are new in the literatureLA engLK http://arxiv.org/pdf/1506.07752v1.pdfOL 30